What is x+3y+3z=2,3x+9y+3z=3,3x+6y+6z=4 ?

The solution to x+3y+3z=2,3x+9y+3z=3,3x+6y+6z=4 is x=0,y= 1/6 ,z= 1/2

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x+3y+3z=2,3x+9y+3z=3,3x+6y+6z=4

x + 3 y + 3 z = 2, 3 x + 9 y + 3 z = 3, 3 x + 6 y + 6 z = 4

x = 0, y = \frac{1}{6}, z = \frac{1}{2}

Solution steps

x + 3 y + 3 z = 2 3 x + 9 y + 3 z = 3 3 x + 6 y + 6 z = 4

Isolate

x

for

x + 3 y + 3 z = 2 : x = 2 - 3 y - 3 z

Substitute

x = 2 - 3 y - 3 z

[3 (2 - 3 y - 3 z) + 9 y + 3 z = 3 3 (2 - 3 y - 3 z) + 6 y + 6 z = 4]

Simplify

[- 6 z + 6 = 3 - 3 y - 3 z + 6 = 4]

Isolate

z

for

- 6 z + 6 = 3 : z = \frac{1}{2}

Substitute

z = \frac{1}{2}

[- 3 y - 3 \cdot \frac{1}{2} + 6 = 4]

Simplify

[- 3 y + \frac{9}{2} = 4]

Isolate

y

for

- 3 y + \frac{9}{2} = 4 : y = \frac{1}{6}

For

x = 2 - 3 y - 3 z

Substitute

y = \frac{1}{6}, z = \frac{1}{2}

x = 2 - 3 \cdot \frac{1}{6} - 3 \cdot \frac{1}{2}

2 - 3 \cdot \frac{1}{6} - 3 \cdot \frac{1}{2} = 0

x = 0

The solutions to the system of equations are:

x = 0, y = \frac{1}{6}, z = \frac{1}{2}

\frac{( 2 x )}{9} + \frac{y}{6} = 2, \frac{x}{a} - \frac{y}{b} = 4

\frac{2 x - 3}{4 y} = 3, x - 4 y + 7 = 0

5 x - y = 3, 5 x + y = 13

y + 10 x = 2 y + 16, x = 5

2 x + y = 6, 3 x - y = 18

What is x+3y+3z=2,3x+9y+3z=3,3x+6y+6z=4 ?
The solution to x+3y+3z=2,3x+9y+3z=3,3x+6y+6z=4 is x=0,y= 1/6 ,z= 1/2